Physics

In this work we apply a novel, accurate, fast, and robust physics-informed neural network framework for data-driven parameters discovery of problems modeled via parametric ordinary differential equations (ODEs) called the Extreme Theory of Functional Connections (X-TFC). The proposed method merges two recently developed frameworks for solving problems involving parametric DEs, 1) the Theory of Functional Connections (TFC) and 2) the Physics-Informed Neural Networks (PINN). In particular, this work focuses on the capability of X-TFC in solving inverse problems to estimate the parameters governing the epidemiological compartmental models via a deterministic approach. The epidemiological compartmental models treated in this work are Susceptible-Infectious-Recovered (SIR), Susceptible-Exposed-Infectious-Recovered (SEIR), and Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIR). The results show the low computational times, the high accuracy and effectiveness of the X-TFC method in performing data-driven parameters discovery of systems modeled via parametric ODEs using unperturbed and perturbed data.

The data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a probabilistic perspective that simultaneously identifies predictive, lower-dimensional coarse-grained (CG) variables as well as their dynamics. We make use of the expressive ability of deep neural networks in order to represent the right-hand side of the CG evolution law. Furthermore, we demonstrate how domain knowledge that is very often available in the form of physical constraints (e.g. conservation laws) can be incorporated with the novel concept of virtual observables. Such constraints, apart from leading to physically realistic predictions, can significantly reduce the requisite amount of training data which enables reducing the amount of required, computationally expensive multiscale simulations (Small Data regime). The proposed state-space model is trained using probabilistic inference tools and, in contrast to several other techniques, does not require the prescription of a fine-to-coarse (restriction) projection nor time-derivatives of the state variables. The formulation adopted is capable of quantifying the predictive uncertainty as well as of reconstructing the evolution of the full, fine-scale system which allows to select the quantities of interest a posteriori. We demonstrate the efficacy of the proposed framework in a high-dimensional system of moving particles.

High-dimensional optimization is a critical challenge for operating large-scale scientific facilities. We apply a physics-informed Gaussian process (GP) optimizer to tune a complex system by conducting efficient global search. Typical GP models learn from past observations to make predictions, but this reduces their applicability to new systems where archive data is not available. Instead, here we use a fast approximate model from physics simulations to design the GP model. The GP is then employed to make inferences from sequential online observations in order to optimize the system. Simulation and experimental studies were carried out to demonstrate the method for online control of a storage ring. We show that the physics-informed GP outperforms current routinely used online optimizers in terms of convergence speed, and robustness on this task. The ability to inform the machine-learning model with physics may have wide applications in science.

In this paper the physics- (or PDE-) integrated machine learning (ML) framework is investigated. The Navier-Stokes (NS) equations are solved using Tensorflow library for Python via Chorin's projection method. The methodology for the solution is provided, which is compared with a classical solution implemented in Fortran. This solution is integrated with a neural network (NN). Such integration allows one to train a NN embedded in the NS equations without having the target (labeled training) data for the direct outputs from the NN; instead, the NN is trained on the field data (quantities of interest), which are the solutions for the NS equations. To demonstrate the performance of the framework, a case study is formulated: the 2D lid-driven cavity with non-constant velocity-dependent dynamic viscosity is considered. A NN is trained to predict the dynamic viscosity from the velocity fields. The performance of the physics-integrated ML is compared with classical ML framework, when a NN is directly trained on the available data (fields of the dynamic viscosity). Both frameworks showed similar accuracy; however, despite its complexity and computational cost, the physics-integrated ML offers principal advantages, namely: (i) the target outputs (labeled training data) for a NN might be unknown and can be recovered using PDEs; (ii) it is not necessary to extract and preprocess information (training targets) from big data, instead it can be extracted by PDEs; (iii) there is no need to employ a physics- or scale-separation assumptions to build a closure model. The advantage (i) is demonstrated in this paper, while the advantages (ii) and (iii) are the subjects for future work. Such integration of PDEs with ML opens a door for a tighter data-knowledge connection, which may potentially influence the further development of the physics-based modelling with ML for data-driven thermal fluid models.

We formulate Wannier orbital overlap population and Wannier orbital Hamilton population to describe the contribution of different orbitals to electron distribution and their interactions. These methods, which are analogous to the well known crystal orbital overlap population and crystal orbital Hamilton population, provide insight into the distribution of electrons at various atom centres and their bonding nature. We apply this formalism in the context of a plane-wave density functional theory calculation. This method provides a means to connect the non-local plane-wave basis to a localised basis by projecting the wave functions from a plane-wave density functional theory calculation on to localized Wannier orbital basis. The main advantage of this formulation is that the spilling factor is strictly zero for insulators and can systematically be made small for metals. We use our proposed method to study and obtain bonding and electron localization insights in five different materials.

Population control is an essential component of any projector Monte Carlo algorithm. This control mechanism usually introduces a bias in the sampled quantities that is inversely proportional to the population size. In this paper, we investigate the population control bias in the full configuration interaction quantum Monte Carlo method. We identify the precise origin of this bias and quantify it in general. We show that it has different effects on different estimators and that the shift estimator is particularly susceptible. We derive a re-weighting technique, similar to the one used in diffusion Monte Carlo, for correcting this bias and apply it to the shift estimator. We also show that by using importance sampling, the bias can be reduced substantially. We demonstrate the necessity and the effectiveness of applying these techniques for sign-problem-free systems where this bias is especially notable. Specifically, we show results for large one-dimensional Hubbard models and the two-dimensional Heisenberg model, where corrected FCIQMC results are comparable to the other high-accuracy results.

WarpX is a general purpose electromagnetic particle-in-cell code that was originally designed to run on many-core CPU architectures. We describe the strategy followed to allow WarpX to use the GPU-accelerated nodes on OLCF's Summit supercomputer, a strategy we believe will extend to the upcoming machines Frontier and Aurora. We summarize the challenges encountered, lessons learned, and give current performance results on a series of relevant benchmark problems.

In numerical investigations of stringent problems in science and engineering research, non-physical negative density or pressure may emerge and cause blow-ups of the computation. We build on the realization that the positivity of density and pressure can be preserved in an efficient way of exploiting the advantage of discontinuous Galerkin and finite volume (DG/FV) hybrid computation framework. We thus present an effective and simple method with great practical significance to maintain the positivity of density and pressure in solving the reactive Euler equations. The approach is able to maximize the multiscale capability of the DG method by achieving both positivity-preserving and oscillation-free solution in the subgrid level. In the designed scheme, a priori detection and computation with hyperbolic tangent function prevent the occurrence of negativity in the flux evaluation, while a posteriori detection and computation with the first-order Godunov scheme guarantee the positivity of subcell solution. The a priori computation achieves bounded reconstruction and less oscillatory solution so that the a posteriori computation can be active in few cells where the extremely complex computation condition appears. Furthermore, the valuable information from the reconstruction process is utilized to design the indication strategy that identifies the DG and FV cells, and the technique of adaptively choosing reconstruction candidates is adopted to overcome the excessive numerical dissipation in the shock-capturing scheme. Numerical tests, including demanding examples in stiff detonation simulation, demonstrate the positivity-preserving, non-oscillatory and subcell resolution property of the present method.

Recent calculations using coupled cluster on solids have raised discussion of using a N −1/3 power law to fit the correlation energy when extrapolating to the thermodynamic limit, an approach which differs from the more commonly used N −1 power law which is (for example) often used by quantum Monte Carlo methods. In this paper, we present one way to reconcile these viewpoints. Coupled cluster doubles calculations were performed on uniform electron gases reaching system sizes of 922 electrons for an extremely wide range of densities ( 0.1< r s <100.0 ) to study how the correlation energy approaches the thermodynamic limit. The data were corrected for basis set incompleteness error and use a selected twist angle approach to mitigate finite size error from shell filling effects. Analyzing these data, we initially find that a power law of N −1/3 appears to fit the data better than a N −1 power law in the large system size limit. However, we provide an analysis of the transition structure factor showing that N −1 still applies to large system sizes and that the apparent N −1/3 power law occurs only at low N .

Full Waveform Inversion (FWI) plays a vital role in reconstructing geophysical structures. The Uncertainty Quantification regarding the inversion results is equally important but has been missing out in most of the current geophysical inversions. Mathematically, uncertainty quantification is involved with the inverse Hessian (or the posterior covariance matrix), which is prohibitive in computation and storage for practical geophysical FWI problems. L-BFGS populates as the most efficient Gauss-Newton method; however, in this study, we empower it with the new possibility of accessing the inverse Hessian for uncertainty quantification in FWI. To facilitate the inverse-Hessian retrieval, we put together BFGS (essentially, full-history L-BFGS) with randomized singular value decomposition towards a low-rank approximation of the Hessian inverse. That the rank number equals the number of iterations makes this solution efficient and memory-affordable even for large-scale inversions. Also, based on the adjoint method, we formulate different diagonal Hessian initials as preconditioners and compare their performances in elastic FWI. We highlight our methods with the elastic Marmousi benchmark, demonstrating the applicability of preconditioned BFGS in large-scale FWI and uncertainty quantification.